Problem 1 Consider the function f defined on the interval (–3, 3) by -3

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Problem 1
Consider the function f defined on the interval (-3, 3) by
6+ 2x, -3 < x < 0,
f(x) =
10,
0 < x < 3,
and let g be the periodic-extension of f. That is, let g be the periodic function defined by g(x) = f(x),
-3 < a < 3, and g(x+6) = g(x).
(1) Find the Fourier Series for f. Include the main steps of the integrations in your solution.
(2) Sketch, on one set of axes, the graph of y = g(x) over the interval -9 <x < 9, and the partial sums
of the fourier series for f using the first 2 and the first 3 frequencies (I.e, truncating the series at n=2
and then at n=3).
Transcribed Image Text:Problem 1 Consider the function f defined on the interval (-3, 3) by 6+ 2x, -3 < x < 0, f(x) = 10, 0 < x < 3, and let g be the periodic-extension of f. That is, let g be the periodic function defined by g(x) = f(x), -3 < a < 3, and g(x+6) = g(x). (1) Find the Fourier Series for f. Include the main steps of the integrations in your solution. (2) Sketch, on one set of axes, the graph of y = g(x) over the interval -9 <x < 9, and the partial sums of the fourier series for f using the first 2 and the first 3 frequencies (I.e, truncating the series at n=2 and then at n=3).
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